Two level deck

Hi all.

I can't figure out how to find any relevant info on this. We have a walk-out basement, so we have an upper and lower deck, right on top of each other. I would like to screen in the lower deck, and be able to use it in the rain. This means I need some sort of roof, above the lower deck and under the floor of the upper deck.

What sort of roof/covering do I need? I guess I could put in an actual plywood/asphalt roof, but this seems overkill, since it will not really be supporting weight of snow or anything. Ideas?